Existing techniques to mine periodic patterns in time series data are focused on discovering full-cycle periodic patterns from an entire time series. However, many useful partial periodic patterns are hidden in long and complex time series data. In this paper, we aim to discover the partial periodicity in local segments of the time series data. We introduce the notion of character density to partition the time series into variable-length fragments and to determine the lower bound of each characters period. We propose a novel algorithm, called DPMiner, to find the dense periodic patterns in time series data. Experimental results on both synthetic and real-life datasets demonstrate that the proposed algorithm is effective and efficient to reveal interesting dense periodic patterns.